34.7.2 Convex Mirrors

FIGURE 34.47 shows parallel light rays approaching a mirror in which the edges curve away from the light source. This is called a convex mirror. In this case, the reflected rays appear to come from a point behind the mirror. This is the focal point for a convex mirror.

FIGURE 34.47 The focal point and focal length of a convex mirror.

The figure illustrates the focal point and focal length of a concave mirror.
FIGURE 34.47 Full Alternative Text

A common example of a convex mirror is a silvered ball, such as a tree ornament. You may have noticed that if you look at your reflection in such a ball, your image appears right-side-up but is quite small. As another example, FIGURE 34.48 shows a city skyline reflected in a polished metal sphere. Let’s use ray tracing to understand why the skyscrapers all appear to be so small.

FIGURE 34.48 A city skyline is reflected in this polished sphere.

A photograph of the reflection of a city skyline on a polished sphere known as the Cloud Gate sculpture in Chicago.

FIGURE 34.49 shows an object in front of a convex mirror. In this case, the reflected rays—each obeying the law of reflection—create an upright image of reduced height behind the mirror. We see that the image is virtual because no rays actually converge at the image point P′. Instead, diverging rays appear to come from this point. Once again, three special rays are enough to find the image.

FIGURE 34.49 A virtual image formed by a convex mirror.

The figure illustrates the virtual image formed by a convex mirror.
FIGURE 34.49 Full Alternative Text

Convex mirrors are used for a variety of safety and monitoring applications, such as passenger-side rearview mirrors and the round mirrors used in stores to keep an eye on the customers. When an object is reflected in a convex mirror, the image appears smaller than the object itself. Because the image is, in a sense, a miniature version of the object, you can see much more of it within the edges of the mirror than you could with an equal-sized flat mirror.

TACTICS BOX 34.4 Ray tracing for a spherical mirror

1 Draw an optical axis. Use graph paper or a ruler! Establish a scale.

2 Center the mirror on the axis. Mark and label the focal point at distance f from the mirror’s surface.

3 Represent the object with an upright arrow at distance s. It’s usually best to place the base of the arrow on the axis and to draw the arrow about half the radius of the mirror.

4 Draw the three “special rays” from the tip of the arrow. All reflections occur at the mirror plane.

  1. A ray parallel to the axis reflects through (concave) or away from (convex) the focal point.

  2. An incoming ray passing through (concave) or heading toward (convex) the focal point reflects parallel to the axis.

  3. A ray that strikes the center of the mirror reflects at an equal angle on the opposite side of the optical axis.

5 Extend the rays forward or backward until they converge. This is the image point. Draw the rest of the image in the image plane. If the base of the object is on the axis, then the base of the image will also be on the axis.

6 Measure the image distance s′. Also, if needed, measure the image height relative to the object height.

Workbook Exercises 28–29

EXAMPLE 34.15 Analyzing a concave mirror

A 3.0-cm-high object is located 60 cm from a concave mirror. The mirror’s focal length is 40 cm. Use ray tracing to find the position and height of the image.

MODEL Use the ray-tracing steps of Tactics Box 34.4.

VISUALIZE FIGURE 34.50 shows the steps of Tactics Box 34.4.

FIGURE 34.50 Ray-tracing diagram for a concave mirror.

The figure illustrates the ray tracing diagram for a concave mirror.

SOLVE We can use a ruler to find that the image position is s′≈120 cm in front of the mirror and its height is h′≈6 cm.

REVIEW The image is a real image because light rays converge at the image point.